In this study we concentrate on high-energy proton–proton collisions that result in the production of an electroweak
\(Z\)  boson (decaying into a pair of muons) in association with one or more jets.
For the jet with the highest transverse momentum, we are going to consider jet angularity observables [1]},
which are variables that probe the energy flow within a jet. Prior to the angularity evaluation we optionally perform the SoftDrop procedure on the candidate jet. The considered jet angularities form an interesting testbed for our theoretical
understanding of intra-jet QCD dynamics. Furthermore, they over great application potential, e.g. in distinguishing
quark-like from gluon-like jets, in a theoretically well-defined way [2]}, [3]}, [4]}, or
in extractions of the strong coupling constant [5]}.
Our analysis begins with a detailed phenomenological study of jet angularities, which is performed exploiting state-of-the-art
Monte Carlo (MC) parton shower simulations. Beside assessing the relative importance of the different contributions that affect the
angularity distributions, such as perturbative radiation, hadronisation and the UE, our studies aim to quantify
the role of modern NLO merging techniques on jet substructure distributions. We then move to the second part of the paper,
where we present first-principle theoretical predictions for the observables of interest. Our resummed calculation is performed
at next-to-leading logarithmic accuracy (NLL) matched to fixed-order predictions evaluated at NLO in \(\alpha _s\) .
Furthermore, by keeping track of the jet flavour in our matching procedure, we are able to obtain what is usually referred to
as \(\text{NLL}^\prime \)  accuracy. We stress that such accuracy is achieved for both the groomed and the ungroomed distributions, which implies
that we account for single-logarithmic corrections originating from soft emissions at wide angle, that we treat as an expansion
in the jet radius parameter, and from non-global logarithms, in the limit of large number of colours (\(N_c\) ).The counting
is different in the case of SoftDrop jets with angular exponent \(\beta =0\)  because only collinear radiation is kept by the groomer
and the resulting distributions are single-logarithmic. In this case, our calculations correctly capture the leading-logarithmic
contributions with non-vanishing coefficients.
Furthermore, our initial detailed study of MC predictions allows us to supplement our perturbative \(\text{NLO} +\text{NLL}  ^\prime \)  predictions
with non-perturbative corrections extracted from hadron-level MC simulations.
Our theoretical predictions are fully differential in the kinematics of the jets and of the leptonic decay products
of the \(Z\)  boson, so that we can impose realistic fiducial cuts and compare them to the distributions obtained from MC
event generators. Our predictions are obtained with the resummation plugin of the SHERPA generator framework [6]}
and they can be directly compared to unfolded measurements from the LHC collaborations, once these become available.We note that similar studies have been performed also in the context of Soft-Collinear Effective Theory (SCET), see e.g. [7]}, [8]}, [9]}, [10]}. To the best of our knowledge, those calculations, when performed for proton–proton collisions, are limited to the leading contribution in the small jet-radius limit.
